- This is basically another formulation of the definition of linear dependence.
- From What does Linear Dependence (or independence) even mean, we understand that a set is linearly dependent if one of the vectors can be expressed as a linear combination of the other vectors in the set.
- If our spans stays the same even if we exclude a vector from it, then that means that our set is linearly dependent.
- The Span is basically the set of all linear combinations, hence if our vector belongs in it, then our vector can be expressed as a linear combination of the other vectors of the spanning set.
- Since our vector can be represented a linear combination of vectors from the spanning set, the spanning set is also linearly dependent.